Co-induction in dynamical systems

Dooley, AH; Zhang, G

Co-induction in dynamical systems

Dooley, AH

Zhang, G

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Publication Type:: Journal Article
Citation:: Ergodic Theory and Dynamical Systems, 2012, 32 (3), pp. 919 - 940
Issue Date:: 2012-06-01

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Field	Value	Language
dc.contributor.author	Dooley, AH https://orcid.org/0000-0002-2656-3042	en_US
dc.contributor.author	Zhang, G	en_US
dc.date.issued	2012-06-01	en_US
dc.identifier.citation	Ergodic Theory and Dynamical Systems, 2012, 32 (3), pp. 919 - 940	en_US
dc.identifier.issn	0143-3857	en_US
dc.identifier.uri	http://hdl.handle.net/10453/114854
dc.description.abstract	If a countable amenable group G contains an infinite subgroup λ, one may define, from a measurable action of λ, the so-called co-induced measurable action of G. These actions were defined and studied by Dooley, Golodets, Rudolph and Sinelsh-chikov. In this paper, starting from a topological action of λ, we define the co-induced topological action of G. We establish a number of properties of this construction, notably, that the G-action has the topological entropy of the λ-action and has uniformly positive entropy (completely positive entropy, respectively) if and only if the λ-action has uniformly positive entropy (completely positive entropy, respectively). We also study the Pinsker algebra of the co-induced action. © 2011 Cambridge University Press.	en_US
dc.relation.ispartof	Ergodic Theory and Dynamical Systems	en_US
dc.relation.isbasedon	10.1017/S0143385711000083	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Co-induction in dynamical systems	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	32	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	closed_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	32	en_US

Abstract:

If a countable amenable group G contains an infinite subgroup λ, one may define, from a measurable action of λ, the so-called co-induced measurable action of G. These actions were defined and studied by Dooley, Golodets, Rudolph and Sinelsh-chikov. In this paper, starting from a topological action of λ, we define the co-induced topological action of G. We establish a number of properties of this construction, notably, that the G-action has the topological entropy of the λ-action and has uniformly positive entropy (completely positive entropy, respectively) if and only if the λ-action has uniformly positive entropy (completely positive entropy, respectively). We also study the Pinsker algebra of the co-induced action. © 2011 Cambridge University Press.

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http://hdl.handle.net/10453/114854